σ-环上一致σ-可加与一致μ-连续的等价性

The Equivalence of Uniform σAdditivityand Uniform μcontinuity on a Ring

讨论了环上的向量测度及其性质，并给出σ－环上的向量测度族的一致σ－可加性与一致μ－连续性的等价性定理，进而得出，域上的向量测度族的一致强可加性与一致μ－连续性也是相互等价的．

The vector measures on a ring and their properties are discussed,and the equivalence theorem for uniform σadditivity and uniform μcontinuity of a family of Xvalued vector measure on a σring is given.